Miscellaneous volumes Choose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables. 70. Volume of a drilled hemisphere Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole of radius 1 is drilled through the center of the hemisphere perpendicular to its base.
Miscellaneous volumes Choose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables. 70. Volume of a drilled hemisphere Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole of radius 1 is drilled through the center of the hemisphere perpendicular to its base.
Solution Summary: The author explains that the volume of the solid is 2sqrt3pi . The intersection of sphere and cylinder is calculated as follows.
Miscellaneous volumesChoose the best coordinate system for finding the volume of the following solids. Surfaces are specified using the coordinates that give the simplest description, but the simplest integration may be with respect to different variables.
70. Volume of a drilled hemisphere Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole of radius 1 is drilled through the center of the hemisphere perpendicular to its base.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
The region in the first quadrant bounded above by x^2=y^3, below by y=0 and on the right by x=8 is revolved around the x axis to generate a solid. Use the shell method to find the volume of the solid.
a) sketch the solid
b) use the shell method to find the volume of the solid
Find the volume of the solid generated by revolving the region bounded by y = 4 − x^2 , y = 3x , and x = 0 about the x axis.
Be sure to do all of the following:
Draw a sketch.
Draw a representative rectangle, this helps you determine the variable of integration and method.
State method used: disk, washer or shell.
The integral(s) you are using to find the volume.
Clearly work out the integration.
Leave answer in EXACT form. Do NOT give decimals.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY